Some sites require more bandwidth throttling, but a vast majority should not. If you are limited to a small number of requests per day, using a proxy service like Tor may be the only way to go. Keep in mind that the limits are probably set to maintain a manageable level of traffic and not to stop people from scraping the site. So if you're hitting them more than their limit by using proxies, you may take their site down which would be bad for you and them.